untitled

Solution : 4 x^1 32

or ( 22 )x^1 32 , or, 22 x^2 25

? 2 x 2 5 ,

or, 2 x 5  2 , or, 2 x 3

2

3

?x

? Solution is

2

3

x

Exercise 4.1
Simplify (1 – 10) :

1. 6

3 5

3

3 ˜ 3

2.

2 125

5 8

4

3

˜

˜

3. 4

3 3

3 3

7 7





u

u

4.

7

(^372) ˜ (^37)
5.( 2 ^1  5 ^1 )^1 6. ( 2 a^1  3 b^1 )^1 7.
2
2
2 1
6 ̧
̧
¹
·
̈ ̈
©
§


a
ab

8. x^1 y˜ y^1 z˜ z^1 x,(x! 0 ,y! 0 ,z! 0 ) 9.
   2 2

2 42

2

4 1

y

 ˜



 

n

n n

10. 1 1

1

1

1

( 3 )

3

( 2 )

3

 







y m m

m

mm

m

Prove (11 – 18) :

11. 2 1
    2 1

4 1





 n

n

n

12.

50

1

6 10 15

2 3 5 6

2

1 2

˜ ˜

˜ ˜ ˜



  

q p q

p pq pq p

13. ̧ ̧ 1
    ¹

·

̈ ̈

©

§

̧ ̧˜

¹

·

̈ ̈

©

§

̧ ̧˜

¹

·

̈ ̈

©

§

n m

n

n m

m a

a

a

a

a

a

"

" "

14. 2 u 2 u 2 1

  

q

rp

p

qr

r

pq

a

a

a

a

a

a

15. 1

1 1 1

̧ ̧^

¹

·

̈ ̈

©

§

̧ ̧ ˜

¹

·

̈ ̈

©

§

̧ ̧ ˜

¹

·

̈ ̈

©

§ ca

a

bc c

c

ab b

b

a

x

x

x

x

x

x 16. 1

̧

̧

¹

·

̈

̈

©

§

̧ ̧ ˜

¹

·

̈

̈

©

§

̧ ̧ ˜

¹

·

̈

̈

©

§

  ca

a

bc c

c

ab b

b

a

x

x

x

x

x

x

17. ̧ ̧ 1
    ¹

·

̈ ̈

©

§

̧ ̧ u

¹

·

̈ ̈

©

§

̧ ̧ u

¹

·

̈ ̈

©

§

  rpq

p

qrp r

r

pqr q

q

p

x

x

x

x

x

x

18. If ax b,by candcz a, show that xyz 1

Solve (19 – 22) :

19. 4 x 8 20. 22 x^1 128 21.

1 3 2 1

3 3

 

x x

22. 2 x 21 x 3

4.4 Logarithm
Logarithm is used to find the values of exponential expressions. Logarithm is written
in brief as ‘Log’. Product, quotient, etc. of large numbers or quantities can easily be
determined by the help of log.

ȏ‹ˆax ayǡx yȐ